Does Mercury have a balmy spot? From Wikipedia:

Although the daylight temperature at the surface of Mercury is generally extremely high, observations strongly suggest that ice exists on Mercury.

Does that mean there could be a spot on Mercury where a person could stand and it would be a balmy 80° F (27° C)?
Obviously, let's ignore any radiation issues, etc.
 A: The observations of ice are at the poles, in permanently shadowed craters, much as people think there may be stable, solid ice in permanently shadowed regions of the lunar south pole.  While one atom that's -50°C right next to another that's +200°C would equilibrate almost immediately, there will be a very tiny transition zone of temperature between the permanently shadowed crater with ice (if it exists) and the much hotter surface that's in the sun.
However, this would be the temperature of the surface.  When I think of "balmy" I think of palm trees, a warm sun, and a gentle breeze.  There is no atmosphere to speak of on Mercury, so there would be no air in which you would experience this "balmy" surface temperature in the very very narrow transition region.
A: Just to add a bit more to Stuarts answer, Mercury has an axial tilt of only 2 degrees, and no atmosphere to speak of. It is the only planet that has such. What do those 2 things lead to?


*

*If an area at one of the poles has an incline of more than 2 degrees in all directions, it will remain in permanent shadow. If it is near, add the latitude-90 to the angle to get it's accuracy.

*There is no atmosphere, and thus, only light directly from the sun, and indirectly through ground heat transportation could possibly heat an area on the planet.


So, putting both of these together, it stands to reason that a reasonable chance that if there was some kind of a valley near a pole, it could be very cold. 
So, an area that would be "balmy" would need to have some method of combining shadow and light in the right proportion. The ideal thing to do would be to have some sort of an atmosphere. It is possible that a proper habitat could be constructed that would allow for that. But, it would have to account for the slight tilt in the axis, and somehow rotate to different angles depending on where the sun is pointed at that time.
Bottom line is, a large enough habitat could be constructed where it would naturally be heated to 80 degrees inside, but it might take some considerable effort. 
Now, it should be noted that there would be some spot of shade, and another of sunlight. The ground would have some distribution beween them, which would allow for temperature contours. I suspect that they would be fairly small, on the order of a few meters or at most tens of meters, from hot to cold. So that narrow band would probably exist, and would be about the size of your shoes.
